@:It's not hw problem at all, thanks, but can i prove it using more simple way? Your answer about absolute convergence seems to me too complicated ...
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LillyFeb 7 '12 at 14:12

Maybe there is a more simple way, but I didn't find it. Maybe an other user will manage to do this. In any case, the part about absolute convergence is just a little more complicated than the convergence, since question 2 can be solved in the same way than in the first part, and question 1 is just manipulating trigonometrical identities.
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Davide GiraudoFeb 7 '12 at 15:43

@ Davide Giraudo So I have that is no absolute convergence but it is convergent conditionally, right?
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LillyFeb 7 '12 at 19:36